Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
476 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C33 | H(3,𝔽3) |
| commutator | C32 | C2×C32×C9 |
| Frattini, cosocle | C33 | C2×C33 |
| prime radical | C2×C34 | C32 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C33 ◁ C2×C34 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6868 | C2 | direct (N × H) |
| 4. C2×#6868 | C3 | direct (N × H) |
| 7. #6868 | C2×C3 | direct (N × H) |
| 13. C2×C32×C9 | C9 | semidirect |
| 22. C32×C9 | C2×C9 | semidirect |
| 39. C2×C3×C9 | C3×C9 | semidirect |
| 53. C3×C9 | C2×C3×C9 | semidirect |
| 87. C2×C3 | #6868 | direct (N × H) |
| 94. C3 | C2×#6868 | direct (N × H) |
| 98. C2 | C3×#6868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6868 | 2 |
| C2×C33×C9 | 3 |
| C2×C3×C32⋊C9 | 3 |
| C2×#6868 | 3 |